Robust Control and Stability Analysis for Stochastic Systems with Markov Jump

Stochastic systems with Markov jump is a new type of stochastic system in recent years, which is a new field integrated by information, control and Markov process. This paper introduces the research history and the newest research trends of stochastic systems with Markov jump, and presents many widespread theoretical and application problems. Moreover, some new research topics and directions related to stochastic systems with Markov jump are proposed.

[1]  Decision Systems.,et al.  Stochastic stability research for complex power systems , 1980 .

[2]  Xuerong Mao,et al.  Exponential stability of stochastic delay interval systems with Markovian switching , 2002, IEEE Trans. Autom. Control..

[3]  Jessica Fuerst,et al.  Stochastic Differential Equations And Applications , 2016 .

[4]  Xuerong Mao,et al.  Robust stability and controllability of stochastic differential delay equations with Markovian switching , 2004, Autom..

[5]  P. Pakshin.  Robust high moment stabilizing control for stochastic systems with jumps , 2001 .

[6]  Michael Athans,et al.  Command and control (C2) theory: A challenge to control science , 1986 .

[7]  Xuerong Mao,et al.  Stochastic Differential Equations With Markovian Switching , 2006 .

[8]  François Dufour,et al.  On the JLQ problem with uncertainty , 1997, IEEE Trans. Autom. Control..

[9]  X. Mao,et al.  Robust stability of uncertain stochastic differential delay equations , 1998 .

[10]  Shengyuan Xu,et al.  Reduced-order H∞ filtering for stochastic systems , 2002, IEEE Trans. Signal Process..

[11]  J. Kato.  Stability in functional differential equations , 1980 .

[12]  G. Stein,et al.  Multivariable feedback design: Concepts for a classical/modern synthesis , 1981 .

[13]  R. Rogers,et al.  An LQ-solution to a control problem associated with a solar thermal central receiver , 1983 .

[14]  Shengyuan Xu,et al.  H∞ and positive-real control for linear neutral delay systems , 2001, IEEE Trans. Autom. Control..

[15]  D. Hinrichsen,et al.  H∞-type control for discrete-time stochastic systems , 1999 .

[16]  V. Kolmanovskii,et al.  Stability of Functional Differential Equations , 1986 .

[17]  X. Mao,et al.  Asymptotic properties of neutral stochastic differential delay equations , 2000 .

[18]  Shengyuan Xu,et al.  Robust H∞ control for uncertain stochastic systems with state delay , 2002, IEEE Trans. Autom. Control..

[19]  G. Zames.  Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses , 1981 .

[20]  Weihai Zhang,et al.  State Feedback HINFINITY Control for a Class of Nonlinear Stochastic Systems , 2006, SIAM J. Control. Optim..

[21]  J. P. Lasalle.  The stability of dynamical systems , 1976 .